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On the Existence and Uniqueness of Solution to Fractional-Order Langevin Equation

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  • Ahmed Salem
  • Noorah Mshary

Abstract

In this work, we give sufficient conditions to investigate the existence and uniqueness of solution to fractional-order Langevin equation involving two distinct fractional orders with unprecedented conditions (three-point boundary conditions including two nonlocal integrals). The problem is introduced to keep track of the progress made on exploring the existence and uniqueness of solution to the fractional-order Langevin equation. As a result of employing the so-called Krasnoselskii and Leray-Schauder alternative fixed point theorems and Banach contraction mapping principle, some novel results are presented in regarding to our main concern. These results are illustrated through providing three examples for completeness.

Suggested Citation

  • Ahmed Salem & Noorah Mshary, 2020. "On the Existence and Uniqueness of Solution to Fractional-Order Langevin Equation," Advances in Mathematical Physics, Hindawi, vol. 2020, pages 1-11, October.
    • Handle: RePEc:hin:jnlamp:8890575
    DOI: 10.1155/2020/8890575
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    Cited by:

    1. Ahmed Salem & Kholoud N. Alharbi & Hashim M. Alshehri, 2022. "Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space," Mathematics, MDPI, vol. 10(8), pages 1-17, April.
    2. Ahmed Salem & Rawia Babusail, 2022. "Finite-Time Stability in Nonhomogeneous Delay Differential Equations of Fractional Hilfer Type," Mathematics, MDPI, vol. 10(9), pages 1-14, May.

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